J

J is a high-level, general-purpose programming language that descended directly from APL (A Programming Language). Created by Kenneth Iverson and Roger Hui, J preserves APL’s powerful array programming paradigm while replacing the special character set with ASCII characters, making it accessible on any standard keyboard.

History & Origins

The story of J begins with Kenneth Iverson’s desire to improve upon his earlier creation, APL. While APL was revolutionary, its reliance on special characters created practical problems: specialized keyboards, display limitations, and portability issues across systems.

The Birth of J

One summer weekend in 1989, Arthur Whitney visited Kenneth Iverson at Kiln Farm in Ontario, Canada. In a single afternoon, Whitney produced a one-page interpreter prototype on an AT&T 3B1 computer. Roger Hui then took this seed and, on Sunday, August 27, 1989, wrote the first line of code that would become J’s implementation.

By August 1990, J was publicly released. Iverson and Hui, along with Eric Iverson (Ken’s son), founded Iverson Software Inc. in February 1990 to develop and distribute the language.

ASCII Revolution

J’s most significant departure from APL was its use of ASCII characters. Where APL used ⍴ (rho) for reshape, J uses $. Where APL used ⌽ for reverse, J uses |.. This made J:

• Usable on any standard keyboard
• Portable across all computing systems
• Embeddable in plain text files and emails
• Easier to discuss in technical documentation

Why J is Unique

Vocabulary: Verbs, Adverbs, Conjunctions

J uses grammatical terminology to describe its parts of speech:

• Nouns: Data (numbers, arrays, strings)
• Verbs: Functions that act on nouns (+, -, % for division, # for count)
• Adverbs: Modifiers that take a verb and return a new verb (/ for reduce, ~ for reflex)
• Conjunctions: Combine two words to make a new word (. for various compositions)

This terminology reflects J’s philosophical approach: programs are sentences in a mathematical language.

Tacit Programming

J excels at tacit (point-free) programming, where you define functions without explicitly naming their arguments:

1
2
3
4

   sum =: +/          NB. sum is "plus reduce"
   mean =: sum % #    NB. mean is sum divided by count
   mean 1 2 3 4 5
3

The mean function never mentions its argument—it’s defined purely in terms of other operations.

Array-Oriented Operations

Like APL, operations in J naturally apply to entire arrays:

1
2
3
4
5

   2 * 1 2 3 4 5
2 4 6 8 10

   1 2 3 + 10 20 30
11 22 33

No loops needed—the operations simply work on all elements.

Right-to-Left Evaluation

J evaluates expressions from right to left with no operator precedence:

1
2

   2 * 3 + 4
14

This reads as “2 times (3 plus 4)” = 14, not “(2 times 3) plus 4” = 10.

J’s Relationship to APL

J is often called “APL without the funny symbols,” but this undersells its innovations:

J also introduced concepts not present in original APL:

• Gerunds: First-class verb collections
• Forks and Hooks: Composition patterns for tacit definitions
• Explicit definitions: Clear syntax for complex function definitions

Modern J

Active Development

J is actively maintained by Jsoftware Inc. The J904 release (2022) demonstrates continued development with:

• Cross-platform support (Windows, macOS, Linux, Raspberry Pi)
• Integrated development environments
• Web-based interfaces
• Modern package management

Open Source

In March 2011, the J source code was released under the GNU General Public License, ensuring its future as open-source software.

Available Implementations

The J Community

J has a dedicated community of practitioners, many in quantitative finance and data science. Resources include:

• Jsoftware Wiki - Official documentation
• J Forums - Community discussion
• Learning J - Official tutorial

Getting Started

J programs are typically stored in .ijs files. The typical workflow:

1
2
3
4
5

# Run a J script
jconsole script.ijs

# Start interactive session
jconsole

Continue to the Hello World tutorial to write your first J program.